Velocity free-stream

Values of and m for various configurations are hsted in Table 5-5. The characteristic length is used in both the Nusselt and the Reynolds numbers, and the properties are evaluated at the film temperature = (tio + G)/2. The velocity in the Reynolds number is the undisturbed free-stream velocity. 

Boundary layer flows are a special class of flows in which the flow far from the surface of an object is inviscid, and the effects of viscosity are manifest only in a thin region near the surface where steep velocity gradients occur to satisfy the no-slip condition at the solid surface. The thin layer where the velocity decreases from the inviscid, potential flow velocity to zero (relative velocity) at the sohd surface is called the boundary layer The thickness of the boundary layer is indefinite because the velocity asymptotically approaches the free-stream velocity at the outer edge. The boundaiy layer thickness is conventionally t en to be the distance for which the velocity equals 0.99 times the free-stream velocity. The boundary layer may be either laminar or turbulent. Particularly in the former case, the equations of motion may be simphfied by scaling arguments. Schhchting Boundary Layer Theory, 8th ed., McGraw-HiU, New York, 1987) is the most comprehensive source for information on boundary layer flows. 

Flat Plate, Zero Angle of Ineidenee For flow over a wide, thin flat plate at zero angle of incidence with a uniform free-stream velocity, as shown in Fig. 6-47, the eritieal Reynolds number at which the boundaiy layer becomes turbulent is normally taken to be... 

D = diameter of cylinder or effective width of objecl V = free-stream velocity p = fluid density [L = fluid viscosity... 

Figure 1.25 shows the boundary layer that develops over a flat plate placed in, and aligned parallel to, the fluid having a uniform velocity upstream of the plate. Flow over the wall of a pipe or tube is similar but eventually the boundary layer reaches the centre-line. Although most of the change in the velocity component vx parallel to the wall takes place over a short distance from the wall, it does continue to rise and tends gradually to the value vx in the fluid distant from the wall (the free stream). Consequently, if a boundary layer thickness is to be defined it has to be done in some arbitrary but useful way. The normal definition of the boundary layer thickness is that it is the distance from the solid boundary to the location where vx has risen to 99 per cent of the free stream velocity v . The locus of such points is shown in Figure 1.25. It should be appreciated that this is a time averaged distance the thickness of the boundary layer fluctuates owing to the velocity fluctuations.

The transition from a laminar boundary layer to a turbulent boundary layer occurs at the value Rex = 3.2 x 105. In the Reynolds number Rex the free stream velocity vand the distance x from the leading edge of the plate are used as the characteristic velocity and linear dimension. 

Momentum boundary layer calculations are useful to estimate the skin friction on a number of objects, such as on a ship hull, airplane fuselage and wings, a water surface, and a terrestrial surface. Once we know the boundary layer thickness, occurring where the velocity is 99% of the free-stream velocity, skin friction coefficient and the skin friction drag on the solid surface can be calculated. Estimate the laminar boundary layer thickness of a 1-m-long, thin flat plate moving through a calm atmosphere at 20 m/s. 

If a fluid such as air flows over a flat plate placed with its surface parallel to the stream, particles in the vicinity of the surface are slowed down by viscous forces. Fluid particles adjacent to the surface stick to it and have zero velocity relative to the boundary. Other fluid particles are retarded as a result of sliding over the immobilised particles. The effects of viscous forces originating at the boundary extend for a certain distance (5, the boundary layer thickness). The effects of viscous forces originating at the boundary are not extensive and the velocity soon approaches free stream velocity. 

The boundary conditions are the no slip boundary conditions at y = 0, and the free-stream velocity, that is,... 

Levy, S., Effect of Large Temperature Changes (Including Viscous Heating) upon Laminar Boundary Layers with Variable Free-Stream Velocity , J. Aeronaut. Sci., Vol. 21, No. 7, pp. 459-474,1954. 

The program, as available, will calculate flow over a surface with a varying free-stream velocity and varying surface temperature. These variations are both assumed to be described by a third-order polynomial, i.e., by ... 

It follows from the assumed form of the free-stream velocity distribution that since ... 

Solution. A solution for values of X up to 107 will be considered. Because flow over a flat plate with an isothermal surface is being considered, the free-stream velocity and surface temperature are constant. Therefore, because the boundary is assumed to be turbulent from the leading edge, the inputs to the program are ... 

A consideration of the orders of magnitude of the terms in the momentum equation for boundary layer flow indicates that if u = o(u ), where u is characteristic free-stream velocity, then the buoyancy force term will be important if ... 

The numerical procedure described above for solving the laminar boundary layer equations is easily extended to deal with situations in which the free-stream velocity is varying with x, i.e., to deal with situations involving flow over bodies of arbitrary shape. 

Consider the boundary-layer flow system shown in Fig. 5-5. The free-stream velocity outside the boundary layer is uand the boundary-layer thickness is... 

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